WASHINGTON — President Obama’s re-election was at once a deeply personal triumph and a victory for the younger, highly diverse and broadly progressive America that rallied to him. It was a result that ought to settle the bitter argument that ground the nation’s government to a near-standstill.

The president spent much of the year fighting the effects of a stubbornly sluggish economic recovery and facing implacable opposition among Republicans in Congress who made defeating him a high priority. He fought back by undermining Mitt Romney’s major asset as a private-equity specialist and by enlisting Bill Clinton as his chief explainer.

And he mobilized a mighty army of African-American and Hispanic voters. They were all the more determined to exercise their voting rights after Republicans sought in state after state to make it harder for them to cast ballots. Latino voters turned out overwhelmingly for the president, guaranteeing that immigration reform will be on the next Congress’ agenda.

Just as important for governance over the next four years, the president took on an increasingly militant conservatism intent on vastly reducing the responsibilities of government and cutting taxes even more on the wealthiest Americans. In the process, he built an alliance of moderates and progressives who still believe in government’s essential role in regulating the marketplace and widening the circle of opportunity.

Many have argued that the president ran a “small” and “negative” campaign, and he was certainly not shy about going after Romney. But this misses the extent to which Obama made specific commitments and repeatedly cast the election as a choice between two different philosophical directions.

He was not vague about what he meant. Obama campaigned explicitly on higher taxes for the wealthy as part of a balanced budget deal. He stoutly defended the federal government’s interventions to bring the economy back from the brink — and especially his rescue of the auto companies.

It cannot be forgotten that saving General Motors and Chrysler was the most “interventionist” and “intrusive” economic policy Obama pursued — and it proved to be the most electorally successful of all of his decisions. The auto bailout was key to Obama’s crucial victory in Ohio, where six in 10 voters approved the rescue. Union households in the state voted strongly for the president, and he held his own among working-class whites.

The president also called for higher levels of government spending for job training and education, particularly community colleges. And he spoke repeatedly against turning Medicare into a voucher program and sending Medicaid to the states.

The voters who re-elected the president knew what they were voting for. They also knew what they were voting against. Romney paid a high price for his comments suggesting that “47 percent” of the electorate was hopelessly dependent on government. Writing off nearly half the potential voters is never a good idea. On Tuesday, a clear majority rejected that notion. It rejected as well Rep. Paul Ryan’s categorization of the country as made up of “makers” and “takers.”

Romney tried hard to scramble toward the political middle in the campaign’s final month, and that too should send a signal: In this election, the hard-line ideas of the tea party were rejected not only by those who voted against the Republicans but also by Republicans themselves. And Republicans know that tea party candidates, notably in Indiana and Missouri, helped spoil their chance to take control of the Senate.

Republicans will take solace in their success in holding on to the House of Representatives. But the party as a whole will have to come to terms with its failures to expand beyond its base of older white voters and to translate right-wing slogans into a coherent agenda. Republicans need to have a serious talk with themselves, and they need to change.

All of this strengthens Obama’s hand. The costs are higher now if Republicans just keep saying no. They can no longer use their desire to defeat Obama as a rallying cry. They cannot credibly insist that tax increases can never be part of a solution to the nation’s fiscal problems.

And now Obama will have the strongest argument a politician can offer. Repeatedly, he asked the voters to settle Washington’s squabbles in his favor. On Tuesday, they did. And so a president who took office four years ago on a wave of emotion may now have behind him something more valuable and durable: a majority that thought hard about his stewardship and decided to let him finish the job he had begun.